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| Home > Publications database > Computing Solids: Models, ab-initio methods and supercomputing |
| Book/Proceedings | FZJ-2014-01759 |
; ; ;
2014
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag
Jülich
ISBN: 978-3-89336-912-6
Please use a persistent id in citations: http://hdl.handle.net/2128/8540
Abstract: The computation of solids is challenged by the mutual interaction of its constituting elements, the myriad electrons and ions. The complex interplay produces a continuous stream of new and unexpected phenomena and forms of matter. The extreme range of length, time, energy and entropy scales established in the solid state give rise to a broad range of materials and associated properties. Some solids exhibit useful collective phenomena, such as ferroelectricity, magnetism, superconductivity, in others exotic states of matter such as the heavy fermion state are taken on. Varying external parameters such as the pressure or the doping it is even possible to switch between different ordered phases. Certain classes of solids show interesting metal to insulator transitions or display transversal, quantum and non-equilibrium transport processes, to mention a few of the ubiquitous emergent phenomena. New exotic phases or quantum states may occur for solids in low dimensions or at the nano- and mesoscopic scales. There are literally hundreds of thousands of solids with mostly unexplored properties. Every day, new solids or solid-state systems are synthesised or grown and novel properties are discovered. These solids find applications as present and emergent materials with specially-designed functionalities on which scientific advances in neighbouring disciplines such as metallurgy, materials science, nano-science, chemistry and biology as well as the geo-science rests on. Downstream applications can be found in information technology, green energy, transportation and health, all of enormous benefits to our society. Even to physicists trained in the reductionistic view on nature it sometimes appears to be a miracle that the formation and stability of all solids and their wealth of properties are encoded in the statistical physics and quantum theory of the many electrons in the solid interacting via the Coulomb potential. It is the Schrödinger equation of many electrons which provides the fundamental theoretical concept for the understanding of the large variety of emerging quantum phenomena and processes that could be exploited in future technological devices. The exact analytical or numerical solution of such a Schrödinger equation for a solid is not in sight. Instead, since the formulation of the quantum mechanical many-body problem it remains a challenge to capture the properties of interacting electrons of complex atomic systems like e.g. a crystalline solid by approximate practical methods or effective models with reasonable computational effort. In the past decades powerful theoretical concepts and reliable and predictive computational models have been developed that allow effective approximations. They aim at reducing complexity while retaining those ingredients necessary for a reliable description of the physical effects of the system. The underlying approximations made may be roughly divided into three different classes: realistic model Hamiltonians, that are solved in part with sophisticated and highly specialised analytical or numerical quantum many-body methods such as renormalization group based techniques or quantum Monte Carlo, wave function based methods and ab initio density functional approaches. Computing solids refers to the application of these computational models to the study and prediction of the physical behaviour of solids. It represents an extension of theoretical physics that is based on mathematical models. The concept of computing solids can be used to predict new phenomena, to explore the validity of new concepts, to design new experiments in order to test these new concepts or simply to generate insight. It can be applied to complement and analyse experiments. It provides a powerful alternative to the techniques of experimental science when phenomena are difficult to observe or not observable with currently available techniques or when measurements are difficult, dangerous, expensive or simply impractical. It can be [...]
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